Comment #16 on issue 829 by smi...@gmail.com: Improve simplify() to handle
result from integrate(log(k**2-m**2), k)
http://code.google.com/p/sympy/issues/detail?id=829
simplify works fine on the original monstrosity and the modifications to
simplify made as Mateusz improved polys are (should be) tested so I'm not
sure that adding the following test is necessary. (It is, however, nice to
know that the more efficient as_numer_denom routine allows this to be
computed almost instantaneously, something that was not possible before
that in even minutes of time.) So please mark it as you see fit. My vote
is to just close the issue.
eq=S('''k**13/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**
... 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) - m**13/(-6*k**10*m**2
... + 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**8 - 6*k**2*m**10 + k**12 +
... m**12)*log(k**2 - m**2) + 2*m**13/(-6*k**10*m**2 + 15*k**8*m**4 -
... 20*k**6*m**6 + 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k + m)
... + k*m**12/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**8
... - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) -
... m*k**12/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**8 -
... 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) -
... 40*k**6*m**7/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k + m) -
... 20*k**7*m**6/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) -
... 15*k**4*m**9/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) -
... 15*k**8*m**5/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) -
... 12*k**2*m**11/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k + m) -
... 12*k**10*m**3/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k + m) -
... 6*k**3*m**10/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) -
... 6*k**11*m**2/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) +
... 2*m*k**12/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**8
... - 6*k**2*m**10 + k**12 + m**12)*log(k + m) +
... 6*k**2*m**11/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) +
... 6*k**10*m**3/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) +
... 15*k**5*m**8/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) +
... 15*k**9*m**4/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) +
... 20*k**6*m**7/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k**2 - m**2) +
... 30*k**4*m**9/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k + m) +
... 30*k**8*m**5/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)*log(k + m) -
... 2*k**13/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**8 -
... 6*k**2*m**10 + k**12 + m**12) - 30*k**5*m**8/(-6*k**10*m**2 +
... 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**8 - 6*k**2*m**10 + k**12 +
... m**12) - 30*k**9*m**4/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12) -
... 2*k*m**12/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**8
... - 6*k**2*m**10 + k**12 + m**12) + 12*k**3*m**10/(-6*k**10*m**2 +
... 15*k**8*m**4 - 20*k**6*m**6 + 15*k**4*m**8 - 6*k**2*m**10 + k**12 +
... m**12) + 12*k**11*m**2/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12) +
... 40*k**7*m**6/(-6*k**10*m**2 + 15*k**8*m**4 - 20*k**6*m**6 +
... 15*k**4*m**8 - 6*k**2*m**10 + k**12 + m**12)''')
simplify(eq)
k*log(k**2 - m**2) - 2*k + 2*m*log(k + m) - m*log(k**2 - m**2)
In case anyone needs to rcover that expression, here it is in encoded form:
Copy the text between triple-# and paste it into an interactive session.
###
code = \
r'''begin 666 -
M'XL( .[#@U$"_\672Q*#( R&]SD%RXKC5,#GB;JP3N^_*PE4L3X&9R2N( GD
M&R(_( Q2*B/?G]?#]K0HQ&B;[(F60K.1V"LEND4N5(UVAV8E"M EF@V:S12M
MT.Q^<S5:JK11;'5F_9IRF@D"AQ!Q"(%M2.XA&*#%86AW67"&N+<L6/"XBNEK
MIR@G*]I630?L2-1?;2%RRW@4)37K+PKGJ+%[J%E!MVJ;9/NZ83TE8447PI0S
M.J5B<G D2E)'R/0:P01):F:MNEDMS6+6:A6@TTJUFF>U;$K5*RBS4FL:=HM2
M'9I#J32L9U9J".6]58WSWW*K>C;'K>H"BO=674#9M#J0*_:=!.>H^\>^]-R4
=7Q-?O./\F%_*,\GI,Y[Z=;C@'/H"GF=,E:T,
end
'''
def tug(string):
"""Return text of a uu encoded gzipped text."""
import StringIO, uu, gzip
f1 = StringIO.StringIO()
f2 = StringIO.StringIO()
f2.write(string)
f2.seek(0)
uu.decode(f2, f1)
f2.seek(0)
f2.flush()
f1.seek(0)
text = gzip.GzipFile(fileobj=f1, mode='rb')
msg = text.read()
[f.close() for f in [text, f1, f2]]
return msg
code = tug(code)
import hashlib
if hashlib.md5(str(code)).hexdigest() == \
'6497254d2d424cb113cb172f731bed0e':
sympify(code)
###
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